I have cut my stable down to one bike in hopes to make room for a roadie.
I don't think there is any connection at all between flats and deep v rims (even pinch flats really). The best way to not get flats is to properly seat your tires and tubes, maintain proper air pressure, and don't ride over pointy ****, and if you do ride over pointy **** make sure you stop and clean debris off the tire.
i had the WORST luck with flats on my Dawes Lightning road bike... seriously i think i had 3 or 4 flats and i BARELY rode that thing. my new conversion has deep-v's and i've ridden a couple of hundred miles easy in the past month, no flats so far!! *knock on wood*